Apparent double-layer capacitance

Figure 4. Apparent double-layer capacitance as a function of Eh, determined from cyclic voltammetry. Increase above about +0.45 volts is due to oxidation of platinum. Zero values at ends of scans are artifacts of the method and do not represent true capacitance values. Temperature = 298 + 1 K.

A similar conclusion arises from the capacitance data for the mercury electrode at far negative potentials (q 0), where anions are desorbed. In this potential range, the double-layer capacitance in various electrolytes is generally equal to ca. 0.17 F Assuming that the molecular diameter of water is 0.31 nm, the electric permittivity can be calculated as j = Cd/e0 = 5.95. The data on thiourea adsorption on different metals and in different solvents have been used to find the apparent electric permittivity of the inner layer. According to the concept proposed by Parsons, thiourea can be treated as a probe dipole. It has been cdculated for the Hg electrode that at (7 / = O.fij is equal to 11.4, 5.8, 5.1, and 10.6 in water, methanol, ethanol, and acetone, respectively. 

When one considers a distance scale much smaller than 1 pm, surface roughness also is an issue to observed electrode behavior. The ratio of the microscopic surface area to the projected electrode area is usually designated the roughness factor, and can vary from 1.0 to 5 or so for typical solid electrodes, or much higher for porous electrodes. Capacitance, surface faradaic reactions, adsorption, and electrode kinetics all depend on microscopic area. For example, double-layer capacitance increases with roughness such that the apparent capacitance (C°bs) is larger than the value for a perfectly flat electrode (Cflat) as shown in Equation 10.1 ... 

The capacitances of the HTSC solution interface cited in the literature [153,523] apparently pertain to the total polarization capacitance. To estimate the double-layer capacitance and more correctly describe the equilibria in the surface layer, the results of -potential measurements can, in principle, be used [423], However, these data correspond to the surfaces which have undergone the degradation. 

In general, it is believed that there is a direct relationship between the apparent BET surface area and the double-layer capacitance (DEC) of porous carbons [156-158], Theoretically, such a correlation should be expected. In practice, the situation is more complicated. 

Although it was elear that separation of an interface into surface and bulk components as in Eq, (19) is artifieial and must disappear in a consistent microscopic analysis, electronic effects were initially diseussed in terms of a compact layer and its capacitance C, It was apparent early on that the eleetrons strongly influence double layer properties [28-33],... 

The deviations from ideal capacitative behavior of the double layer at solid electrodes also become apparent in the impedance spectroscopy behavior of electrode reactions at such electrodes where a Faradaic resistance is coupled with the capacitance then, instead of regular semicircular complex-plane plots, the Nyquist plots are arcs of semicircles, i.e. with centers depressed below the Z axis. 

The dashed lines in Fig. 11 show the capacitance of the diffuse double-layer calculated using the Gouy-Chapman theory from Eq. (35) for A cpi = const=0. As it has been noticed [21], two trends are apparent on comparing the experimental capacitances with those calculated using the GC theory. First, at low surface charge... 

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